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At least 1,495 records · Page 83
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DOE OSTI2013

Solvable model of quantum phase transitions and the symbolic-manipulation-based study of its multiply degenerate exceptional points and of their unfolding

It is known that the practical use of non-Hermitian (i.e., typically, PT-symmetric) phenomenological quantum Hamiltonians H≠H{sup †} requires an efficient reconstruction of an ad hoc Hilbert-space metric Θ=Θ(H) which would render the time-evolution unitary. Once one considers just the N-dimensional matrix toy models H=H{sup (N)}, the matrix elements of Θ(H) may be defined via a coupled set of N{sup 2} polynomial equations. Their solution is a typical task for computer-assisted symbolic manipulations. The feasibility of such a model-completion construction is illustrated here via a discrete square well model H=p{sup 2}+V endowed with a k-parametric close-to-the-boundary interaction V. The model is shown to possess (possibly, multiply degenerate) exceptional points marking the phase transitions which are attributable, due to the exact solvability of the model at any N<∞, to the loss of the regularity of the metric. In the parameter-dependence of the energy spectrum near these singularities one encounters a broad variety of alternative, topologically non-equivalent scenarios. -- Highlights: •New elementary non-Hermitian quantum Hamiltonians with real spectra proposed. •Exceptional points found and studied. •Non-equivalent stability-loss patterns of phase transition identified. •Hermitization matrices of metrics Θ constructed via symbolic manipulations and extrapolations at all N and k.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2013

On the spin- 1/2 Aharonov–Bohm problem in conical space: Bound states, scattering and helicity nonconservation

In this work the bound state and scattering problems for a spin- 1/2 particle undergone to an Aharonov–Bohm potential in a conical space in the nonrelativistic limit are considered. The presence of a δ-function singularity, which comes from the Zeeman spin interaction with the magnetic flux tube, is addressed by the self-adjoint extension method. One of the advantages of the present approach is the determination of the self-adjoint extension parameter in terms of physics of the problem. Expressions for the energy bound states, phase-shift and S matrix are determined in terms of the self-adjoint extension parameter, which is explicitly determined in terms of the parameters of the problem. The relation between the bound state and zero modes and the failure of helicity conservation in the scattering problem and its relation with the gyromagnetic ratio g are discussed. Also, as an application, we consider the spin- 1/2 Aharonov–Bohm problem in conical space plus a two-dimensional isotropic harmonic oscillator. -- Highlights: •Planar dynamics of a spin- 1/2 neutral particle. •Bound state for Aharonov–Bohm systems. •Aharonov–Bohm scattering. •Helicity nonconservation. •Determination of the self-adjoint extension parameter.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2014

Effective dynamics of a classical point charge

The effective Lagrangian of a point charge is derived by eliminating the electromagnetic field within the framework of the classical closed time path formalism. The short distance singularity of the electromagnetic field is regulated by an UV cutoff. The Abraham–Lorentz force is recovered and its similarity to quantum anomalies is underlined. The full cutoff-dependent linearized equation of motion is obtained, no runaway trajectories are found but the effective dynamics shows acausality if the cutoff is beyond the classical charge radius. The strength of the radiation reaction force displays a pole in its cutoff-dependence in a manner reminiscent of the Landau-pole of perturbative QED. Similarity between the dynamical breakdown of the time reversal invariance and dynamical symmetry breaking is pointed out. -- Highlights: •Extension of the classical action principle for dissipative systems. •New derivation of the Abraham–Lorentz force for a point charge. •Absence of a runaway solution of the Abraham–Lorentz force. •Acausality in classical electrodynamics. •Renormalization of classical electrodynamics of point charges.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Critical coupling and coherent perfect absorption for ranges of energies due to a complex gain and loss symmetric system

We consider a non-Hermitian medium with a gain and loss symmetric, exponentially damped potential distribution to demonstrate different scattering features analytically. The condition for critical coupling (CC) for unidirectional wave and coherent perfect absorption (CPA) for bidirectional waves are obtained analytically for this system. The energy points at which total absorption occurs are shown to be the spectral singular points for the time reversed system. The possible energies at which CC occurs for left and right incidence are different. We further obtain periodic intervals with increasing periodicity of energy for CC and CPA to occur in this system. -- Highlights: •Energy ranges for CC and CPA are obtained explicitly for complex WS potential. •Analytical conditions for CC and CPA for PT symmetric WS potential are obtained. •Conditions for left and right CC are shown to be different. •Conditions for CC and CPA are shown to be that of SS for the time reversed system. •Our model shows the great flexibility of frequencies for CC and CPA.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Thermodynamic properties of asymptotically Reissner–Nordström black holes

Motivated by possible relation between Born–Infeld type nonlinear electrodynamics and an effective low-energy action of open string theory, asymptotically Reissner–Nordström black holes whose electric field is described by a nonlinear electrodynamics (NLED) are studied. We take into account a four dimensional topological static black hole ansatz and solve the field equations, exactly, in terms of the NLED as a matter field. The main goal of this paper is investigation of thermodynamic properties of the obtained black holes. Moreover, we calculate the heat capacity and find that the nonlinearity affects the minimum size of stable black holes. We also use Legendre-invariant metric proposed by Quevedo to obtain scalar curvature divergences. We find that the singularities of the Ricci scalar in Geometrothermodynamics (GTD) method take place at the Davies points. -- Highlights: •We examine the thermodynamical properties of black holes in Einstein gravity with nonlinear electrodynamics. •We investigate thermodynamic stability and discuss about the size of stable black holes. •We obtain analytical solutions of higher dimensional theory.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2014

Lectures on renormalization and asymptotic safety

A short introduction is given on the functional renormalization group method, putting emphasis on its nonperturbative aspects. The method enables to find nontrivial fixed points in quantum field theoretic models which make them free from divergences and leads to the concept of asymptotic safety. It can be considered as a generalization of the asymptotic freedom which plays a key role in the perturbative renormalization. We summarize and give a short discussion of some important models, which are asymptotically safe such as the Gross–Neveu model, the nonlinear σ model, the sine–Gordon model, and we consider the model of quantum Einstein gravity which seems to show asymptotic safety, too. We also give a detailed analysis of infrared behavior of such scalar models where a spontaneous symmetry breaking takes place. The deep infrared behavior of the broken phase cannot be treated within the framework of perturbative calculations. We demonstrate that there exists an infrared fixed point in the broken phase which creates a new scaling regime there, however its structure is hidden by the singularity of the renormalization group equations. The theory spaces of these models show several similar properties, namely the models have the same phase and fixed point structure. The quantum Einstein gravity also exhibits similarities when considering the global aspects of its theory space since the appearing two phases there show analogies with the symmetric and the broken phases of the scalar models. These results be nicely uncovered by the functional renormalization group method.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Solutions on a brane in a bulk spacetime with Kalb–Ramond field

Effective gravitational field equations on a brane have been derived, when the bulk spacetime is endowed with the second rank antisymmetric Kalb–Ramond field. Since both the graviton and the Kalb–Ramond field are closed string excitations, they can propagate in the bulk. After deriving the effective gravitational field equations on the brane, we solve them for a static spherically symmetric solution. It turns out that the solution so obtained represents a black hole or naked singularity depending on the parameter space of the model. The stability of this model is also discussed. Cosmological solutions to the gravitational field equations have been obtained, where the Kalb–Ramond field is found to behave as normal pressure free matter. For certain specific choices of the parameters in the cosmological solution, the solution exhibits a transition in the behaviour of the scale factor and hence a transition in the expansion history of the universe. The possibility of accelerated expansion of the universe in this scenario is also discussed.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2018

Quantum simulation of discrete curved spacetime by the Bose–Hubbard model: From analog acoustic black hole to quantum phase transition

We present a theoretical scheme to simulate quantum field theory in a discrete curved spacetime based on the Bose–Hubbard model describing a Bose–Einstein condensate trapped inside an optical lattice. Using the Bose–Hubbard Hamiltonian, we first introduce a hydrodynamic presentation of the system evolution in discrete space. We then show that the phase (density) fluctuations of the trapped bosons inside an optical lattice in the superfluid (Mott insulator) state obey the Klein–Gordon equation for a massless scalar field propagating in a discrete curved spacetime. We derive the effective metrics associated with the superfluid and Mott-insulator phases and, in particular, we find that in the superfluid phase the metric exhibits a singularity which can be considered as the manifestation of an analog acoustic black hole. The proposed approach is found to provide a suitable platform for quantum simulation of various spacetime metrics through adjusting the system parameters.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Schrödinger potentials solvable in terms of the general Heun functions

Highlights: •There are 35 Schrödinger potentials solvable in terms of the Heun functions. •Only 11 of the potentials are independent. •9 potentials have sub-potentials with solution via a single hypergeometric function. •Many subpotentials are solved through a combination of two hypergeometric functions. •A generalization of the third exactly solvable hypergeometric potential is presented. -- Abstract: We show that there exist 35 choices for the coordinate transformation each leading to a potential for which the stationary Schrödinger equation is exactly solvable in terms of the general Heun functions. Because of the symmetry of the Heun equation with respect to the transposition of its singularities only eleven of these potentials are independent. Four of these independent potentials are always explicitly written in terms of elementary functions, one potential is given through the Jacobi elliptic sn-function, and the others are in general defined parametrically. Nine of the independent potentials possess exactly or conditionally integrable hypergeometric sub-potentials for which each of the fundamental solutions of the Schrödinger equation is written through a single hypergeometric function. Many of the potentials possess sub-potentials for which the general solution is written through fundamental solutions each of which is a linear combination of two or more Gauss hypergeometric functions. We present an example of such a potential which is a conditionally integrable generalization of the third exactly solvable Gauss hypergeometric potential.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Three examples of quantum dynamics on the half-line with smooth bouncing

This article is an introductory presentation of the quantization of the half-plane based on affine coherent states (ACS). The half-plane carries a natural affine symmetry, i.e. it is a homogeneous space for the 1d-affine group, and it is viewed as the phase space for the dynamics of a positive physical quantity evolving with time. Its affine symmetry is preserved due to the covariance of this type of quantization. We promote the interest of such a procedure for transforming a classical model into a quantum one, since the singularity at the origin is systematically removed, and the arbitrariness of boundary conditions for the Schrödinger operator can be easily overcome. We explain some important mathematical aspects of the method. Three elementary examples of applications are presented, the quantum breathing of a massive sphere, the quantum smooth bouncing of a charged sphere, and a smooth bouncing of “dust” sphere as a simple model of quantum Newtonian cosmology.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Static and spherically symmetric solutions in a scenario with quadratic curvature contribution

In this work we investigate analytic static and spherically symmetric solutions of a generalized theory of gravity in the Einstein–Cartan formalism. The main goal consists in analysing the behaviour of the solutions under the influence of a quadratic curvature term in the presence of cosmological constant and no torsion. In the first incursion we found an exact de Sitter-like solution. This solution is obtained by imposing vanishing torsion in the field equations. On the other hand, by imposing vanishing torsion directly in the action, we are able to find a perturbative solution around the Schwarzschild–de Sitter usual solution. We briefly discuss classical singularities for each solution and the event and cosmological horizons. A primer discussion on the thermodynamics of the geometrical solutions is also addressed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

A phenomenon of splitting resonant-tunneling one-point interactions

The so-called δ'-interaction as a particular example in Kurasov’s distribution theory developed on the space of discontinuous (at the point of singularity) test functions, is identified with the diagonal transmission matrix, continuously depending on the strength of this interaction. On the other hand, in several recent publications, the δ'-potential has been shown to be transparent at some discrete values of the strength constant and opaque beyond these values. This discrepancy is resolved here on the simple physical example, namely the heterostructure consisting of two extremely thin layers separated by infinitesimal distance. In the three-scale squeezing limit as the thickness of the layers and the distance between them simultaneously tend to zero, a whole variety of single-point interactions is realized. The key point is the generalization of the δ'-interaction to the family for which the resonance sets appear in the form of a countable number of continuous two-dimensional curves. In this way, the connection between Kurasov’s δ'-interaction and the resonant-tunneling point interactions is derived and the splitting of the resonance sets for tunneling plays a crucial role.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Electronic optics in graphene in the semiclassical approximation

Highlights: • A rigorous semiclassical theory for the two-dimensional Dirac equation is developed. • We discuss how the use of eikonal coordinates greatly simplifies the theory. • Electronic optics in graphene is developed beyond the standard WKB approximation. • The semiclassical phase essentially affects electron focusing in graphene. - Abstract: We study above-barrier scattering of Dirac electrons by a smooth electrostatic potential combined with a coordinate-dependent mass in graphene. We assume that the potential and mass are sufficiently smooth, so that we can define a small dimensionless semiclassical parameter h≪1. This electronic optics setup naturally leads to focusing and the formation of caustics, which are singularities in the density of trajectories. We construct a semiclassical approximation for the wavefunction in all points, placing particular emphasis on the region near the caustic, where the maximum of the intensity lies. Because of the matrix character of the Dirac equation, this wavefunction contains a nontrivial semiclassical phase, which is absent for a scalar wave equation and which influences the focusing. We carefully discuss the three steps in our semiclassical approach: the adiabatic reduction of the matrix equation to aneffective scalar equation, the construction of the wavefunction using the Maslov canonical operator and the application of the uniform approximation to the integral expression for the wavefunction in the vicinity of a caustic. We consider several numerical examples and show that our semiclassical results are in very good agreement with the results of tight-binding calculations. In particular, we show that the semiclassical phase can have a pronounced effect on the position of the focus and its intensity.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

Classical defocussing of world lines in higher dimensions

A five-dimensional gravity theory, motivated by the brane-world picture, with Kaluza scalar in the 5-dimensional metric as g{sub 55}(r);r=√(x{sup 2}+y{sup 2}+z{sup 2}), is considered near the possible singularity (small distance scales where gravity is strong) and is shown to give rise to a positive contribution to the Raychaudhuri equation. This inhibits the focusing of world lines and contributes to non-focusing of the worldlines in the 5-dimensional space. It is also shown that the results extend to time dependent cases such as those relevant for black hole interiors and cosmology.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2019

Covariant action for bouncing cosmologies in modified Gauss–Bonnet gravity

Cyclic universes with bouncing solutions are candidates for solving the big bang initial singularity problem. Here we seek bouncing solutions in a modified Gauss–Bonnet gravity theory, of the type R+f(G), where R is the Ricci scalar, G is the Gauss–Bonnet term, and f some function of it. In finding such a bouncing solution we resort to a technique that reduces the order of the differential equations of the R+f(G) theory to second-order equations. As general relativity is a theory whose equations are of second-order, this order reduction technique enables one to find solutions which are perturbatively close to general relativity. We also build the covariant action of the order reduced theory.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2019

Relativistic strange stars in Tolman–Kuchowicz spacetime

Highlights: • We study relativistic strange star using Tolman–Kuchowicz metric. • Bag constant (55–75) MeV/fm{sup 3} remains within the predicted range for stable strange star. • Using observed values for mass and radius, we calculate different physical parameters. • This model satisfies energy conditions, TOV equations and all other stability criteria. • Solutions are completely free from any singularity and give stable stellar system. - Abstract: In this article we propose a relativistic model of a static spherically symmetric anisotropic strange star with the help of Tolman–Kuchowicz (TK) metric potentials (Tolman, 1939 and Kuchowicz, 1968). The form of the potentials are λ(r)=ln(1+ar{sup 2}+br{sup 4}) and ν(r)=Br{sup 2}+2lnC where a, b, B and C are constants which we have to evaluate using boundary conditions. We also consider the simplest form of the phenomenological MIT bag equation of state (EOS) to represent the strange quark matter (SQM) distribution inside the stellar system. Here, the radial pressure p{sub r} relates with the density profile ρ as follows, p{sub r}(r)=(1/3)[ρ(r)−4B{sub g}], where B{sub g} is the Bag constant. To check the physical acceptability and stability of the stellar system based on the obtained solutions, we have performed various physical tests. It is shown that the model satisfies all the stability criteria, including nonsingular nature of the density and pressure, implies stable nature. Here, the Bag constant for different strange star candidates are found to be (68–70) MeV/fm{sup 3} which satisfies all the acceptability criteria and remains in the experimental range.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2019

Slow expansion in the scalar-tensor theory of gravity

In this paper, we analyze the slow expansion scenario in the scalar-tensor theory of gravity. After considering the slow expansion solution H≃0, we discuss the slow expansion in the scalar-tensor theory by terms of the nearly scale-invariant primordial power spectrum and find that the primordial power spectrum can be determined by the coupling function f(φ). After the slow expansion phase ends, general relativity can be recovered under certain conditions, and then the universe evolves in accordance with the standard cosmology. In the scalar-tensor theory, the slow expansion scenario provides a possible way to avoid the big bang singularity.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Some aspects of the five-dimensional Lovelock black hole spacetime: Strong homotopy retract, perihelion precession and quasistationary levels

Highlights: • Some topological aspects are explored. • The perihelion precession is calculated. • The general Heun functions are applied to obtain analytical solutions. • The quasibound states and the radial wave eigenfunctions are obtained. In this work we explore some mathematical physics aspects of the spherically symmetric Lovelock black hole in high dimensions. Intended for this aim, we thoroughly consider the metric corresponding to the five-dimensional Lovelock black hole spacetime. We construct the strong retractions by the geodesic equations on the background under consideration. As a result, from the topological point of view, we construct the theory of strong homotopy retract, which will allow us, in principle, to better understand some of its suitable applications on astrophysics and cosmology, in particular, in the analysis of the spacetime singularities. We find the solutions of the equation of motion for both radial and angular coordinates, and then we describe the outer (“exterior”) and lower (“interior”) apparent horizons. Indeed, the outer apparent horizon is the last surface from which the light waves could still escape from the black hole. Thus, it is meaningful to analyze some physical phenomena related to quantum particles propagating outside the exterior apparent horizon, in particular, we discuss the quasistationary levels of scalar fields and their radial wave functions, which are given in terms of the general Heun functions. We also calculate the perihelion precession in this background.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗